Effect of Physical Nature (Intact and Powder) of Coal on CO2 Adsorption at the Subcritical Pressure Range (up to 6.4 MPa at 298.15 K)

This study examines the influence of subcritical pressure and the physical nature (intact and powder) of coal samples on CO2 adsorption capacity and kinetics in the context of CO2 sequestration in shallow level coal seams. Manometric adsorption experiments were carried out on two anthracite and one bituminous coal samples. Isothermal adsorption experiments were carried out at 298.15 K in two pressure ranges: less than 6.1 MPa and up to 6.4 MPa relevant to gas/liquid adsorption. The adsorption isotherms of intact anthracite and bituminous samples were compared to that of the powdered samples. The powdered samples of the anthracitic samples had a higher adsorption than that of intact samples due to the exposed adsorption sites. The intact and powdered samples of bituminous coal, on the other hand, exhibited comparable adsorption capacities. The comparable adsorption capacity is attributed to the intact samples’ channel-like pores and microfractures, where high density CO2 adsorption occurs. The adsorption–desorption hysteresis patterns and the residual amount of CO2 trapped in the pores reinforce the influence of the physical nature of the sample and pressure range on the CO2 adsorption–desorption behavior. The intact 18 ft AB samples showed significantly different adsorption isotherm pattern to that of powdered samples for experiments conducted up to 6.4 MPa equilibrium pressure due to the high-density CO2 adsorbed phase in the intact samples. The adsorption experimental data fit into the theoretical models showed that the BET model fit better than the Langmuir model. The experimental data fit into the pseudo first order, second order, and Bangham pore diffusion kinetic models showed that the rate-determining steps are bulk pore diffusion and surface interaction. Generally, the results obtained from the study demonstrated the significance of conducting experiments with large, intact core samples pertinent to CO2 sequestration in shallow coal seams.


INTRODUCTION
Geological carbon dioxide (CO 2 ) storage, especially, sequestration in unmineable coal seams, has a high potential owing to higher CO 2 storage capacity. 1,2 Numerous experimental studies have revealed that coal can adsorb and store CO 2 , and coal seams have the potential to store 300−964 Gt CO 2 globally. 1−6 CO 2 storage capacity of coal seams are estimated by considering the experimentally determined adsorption capacity of the various coal ranks as one of the factors. 1 However, the knowledge gap in the effect of sample physical type (intact or powdered) and subcritical pressure range (liquid and gas) on CO 2 adsorption must be improved in order to comprehend the storage potential of the shallow level coal seams.
Adsorption capacity and kinetics of CO 2 adsorption on coal samples are often related to coal rank, moisture content, swelling characteristics, porosity, temperature, and operating pressures. 1,7−9 In general, the CO 2 adsorption capacity of a specific rank of coal increases with pressure and showed decreasing trend in a few studies. 10−15 To maximize storage capacity and safety, supercritical CO 2 injection into coal seams deeper than 500 m has been considered. However, at greater depths, the confining pressure and coal swelling influence the permeability of high-density CO 2 and hinder the storage potential. 16 As a consequence, CO 2 storage at shallower depth coal deposits has received attention, and horizontal injection of subcritical CO 2 in existing shallow level coal mines has been regarded as a technological advance because it improves the CO 2 contact area while reducing the impact of coal swelling. 17 CO 2 adsorption is a gas/liquid phase adsorption at coal seam depths where the temperature and pressure values are less than the critical value (31°C and 7.38 MP). 18−21 The density of CO 2 is extremely sensitive near the critical point (van der Waals loop region) where the coexistence of liquid and vapor phases would influence the way coal-CO 2 interaction occurs in general. 14,22 Adsorption capacity and kinetics data on intact coal samples are limited for the subcritical range 20,23−25 due to the difficulties with core sample extraction, extended time needed to achieve equilibrium, variable permeability, and pore diffusion/condensation. 24 Moreover, pulverizing coal samples can alter or lose their physical nature, which affects their CO 2 adsorption properties. 26−28 Consequently, it stands to reason that comparing the CO 2 adsorption capacity of intact and powdered samples of various coal ranks would reveal the effect of the sample's physical type on CO 2 adsorption. Therefore, more laboratory investigations with intact coal samples at subcritical temperature and pressure region are fundamental to understanding coal-CO 2 interactions.
Methane desorption was widely focused on in previous works, 29−31 the CO 2 desorption data are less discussed in the literature, and it is important to investigate the reversibility of pore trapped CO 2 . The pore trapping mechanisms such as pore blockage, gas cavitation, adsorption induced deformation, and pore network (ink bottle effect) affect the adsorption− desorption hysteresis pattern and correlate with the coal rank. 32 In general, a limited number of studies modeled the desorption kinetics. 32,33 Among the two dominant kinetic models, pseudo-first order (PFO) and pseudo-second order (PSO), the PSO model agreed well with the experimental results obtained using a manometric adsorption experimental set up for an intact and powdered bituminous coal sample, implying that CO 2 adsorption kinetics and hysteresis were determined by pore diffusion and condensation. 34,35 Njikam and Schiewer (2012) 36 modified the commonly used adsorption kinetic models (PFO and PSO) to adopt the desorption process. These models have not been fully explored for CO 2 adsorption−desorption. 23 The rate-determining steps for the adsorption−desorption process can be predicted by fitting the adsorption−desorption kinetics experimental data in the Bangham pore diffusion model and the modified PFO and PSO equations. 36, 37 While efforts have been made to understand supercritical CO 2 adsorption on powdered samples, the present study seeks to investigate the CO 2 adsorption capacity and kinetics of intact anthracite and bituminous coal samples in comparison to powdered samples, how the adsorption−desorption isotherm hysteresis differs for powder and intact samples in terms of the physical type of coal, and the effects of subcritical and the near critical injection pressure range at 298 K. For this, a manometric gas adsorption experimental setup was employed. The results of adsorption studies utilizing intact and powdered samples of two anthracite coals and a bituminous coal were fitted into theoretical isotherm and kinetic models to determine the CO 2 adsorption mechanism at 298.15 K.

Coal Properties and Sample Preparation.
Coal samples were collected from two coal mines in South Wales Coalfield, Wales, UK. The anthracite coal samples were obtained from the Aberpergwm coal mine (51°44′28.8″N 3°38′36.0″W), while the bituminous coal (water content 0.96%) samples were obtained from the Big Pit National Museum (51.7724°N 3.1050°W). Coal blocks were extracted from the Aberpergwm colliery's two coal seams, the 9 ft seam (with a water content of 0.91%) at a depth of 550 m and the 18 ft seam (water content 0.78%) at a depth of 500 m. The Big Pit coal had a water content of 0.96% and was extracted from a coal seam at a depth of 90 m. These samples will be referred to as 9 ft AB and 18 ft AB and BP hereafter.
The proximate and ultimate analyses were conducted in accordance with the British Standards Institution (BSI) and American Society for Testing Materials (ASTM) standards. 38−43 Table 1 summarizes the analyses. On the basis of carbon content, volatiles, and gross calorific value, the Aberpergwm samples (9 ft AB and 18 ft AB) were classified as anthracite coal (high rank). The Big Pit (BP) sample was identified as low volatile bituminous coal based on their carbon content. 44,45 2.2. Intact and Powdered Sample Preparation and SEM Imaging. Coal cores were drilled from large coal blocks using a core drill machine equipped with a diamond saw-tipped core drilling bit with a 50 mm internal diameter. Samples were air-dried prior to conducting adsorption experiments. Figure 1 illustrates the coal core sample and powdered sample. To prepare powdered samples, coal chunks were pulverized and passed through a 63 μm-mesh screen.
The SEM images of the intact and powdered coal samples were obtained using a Zeiss Sigma HD field emission gun analytical high-resolution SEM (natural samples). The samples were finely gold coated to reduce the charging effect, and the images were used to visualize the structural change in the powder and intact samples of relevant coal rank, as discussed in section 4.1.  Figure 1. Photographs of coal core and powdered samples.

Methodology.
A manometric adsorption apparatus (volumetric) was used in this study. The apparatus was supplied by GDS Instruments, UK. It is capable of operating at pressures up to 20 MPa and temperatures up to 338 K (65°C). Schematic of the manometric sorption apparatus and experimental setup is presented in Figure 2a, and a photograph of the major components is presented in Figure 2b. The test setup instrumentation is as follows: (1) a manometric unit consisting of a reference cell (RC) for storing a known quantity of gas and a sample cell (SC) for storing the adsorbent, (2) needle valves for connecting and isolating the RC and SC, (3) pressure transducers with a resolution of 0.002 MPa (2 kPa) and accuracy of 0.15%, and data loggers, (4) a water bath with a temperature controller for maintaining the temperature of 298.15 K ± 0.01 K, and (5) A calibration cell (volume = 0.0004892 m 3 ) that determines the empty and sample loaded void volumes of RC and SC using the helium pycnometry (Hepycnometry) method. The calibration cell heater is kept at a constant temperature of 298.15 K ± 0.01.
Manometric adsorption is a mass balance technique that utilizes precise pressure, volume, and temperature measurements. 46 The experimental concept is as follows: (i) determine void volumes (v d ) of RC and SC using the He-pycnometry method, (ii) prepare a known quantity of CO 2 gas in RC and expand it into SC while monitoring the pressure drop; repeat the procedure progressively by increasing pressure in RC; and (iii) calculate the adsorbed amount using an appropriate equation of state (EoS) for CO 2 and the perfect gas law.
The He-pycnometry method, which involves injecting He into the adsorption cell at experimental ambient temperature and pressure, can be used to approximate the void volume (v d ) available for gas molecules in the adsorption cell. The void volume (v d ) is calculated via the He-pycnometry method and using the perfect gas law as 46 where n He is the number of moles of He injected (mol), P He is the pressure of He (Pa), T is the absolute temperature (298.15 K), and R is the gas constant (8.314 J/mol·K). The compressibility factor (Z He ) values were calculated using the Peng−Robinson equation of state (PR-EoS). 22 The amount of CO 2 adsorbed or desorbed is calculated as follows: 46 where n ad/de CO 2 is the number of moles of CO 2 adsorbed during adsorption (ad) and desorption (de) (mol; 44.01 g of CO 2 / mol), n t CO 2 is the known amount of CO 2 present in the gas phase (RC + SC) at the beginning of the adsorption or desorption experiment (mol), n e CO 2 amount of CO 2 present in the gas phase (RC + SC) at the equilibrium (end of the adsorption or desorption test) (mol), v d is the void volume available for gas (m 3 ), p rc + sc CO 2 is the initial CO 2 pressure in RC and SC before adsorption, p eq CO 2 is the equilibrium pressure of CO 2 in RC and SC after adsorption (Pa), Z is the compressibility factor of CO 2 , and R is the universal gas constant (R = 8.314 Pa m 3 /K/mol). n t CO 2 is the known amount of CO 2 present in the gas phase (RC + SC) at the beginning of the adsorption experiment (mol).
In this study, the adsorption experiments were conducted by increasing the CO 2 pressure in stages, starting at 0.5 MPa until it reached to a maximum target pressure of 6.5 MPa pressure. CO 2 desorption experiments were conducted using a pressure stepdown procedure from the peak equilibrium pressure to the null pressure. Changes in gas phase pressure were recorded every 10 s to capture the rapid rate of adsorption−desorption at the beginning of the experiment and used to determine the adsorption capacity and kinetics. The experimental program is summarized in Table 2.
The van der Waals loop occurs near the critical pressure range (6.1 to 6.4 MPa at 298.15 K), in which liquid and vapor CO 2 coexist and differ in molar volumes. The CO 2 critical pressure value is 6.4 MPa at 298.15 K. 51 Above this point, the coexistence of liquid and vapor is impossible. This is a key technical aspect that affects adsorption results as an overestimation or underestimation of CO 2 excess adsorption calculations. To overcome this phenomenon, the following theoretical consideration was made in the current study to calculate the amount of CO 2 adsorbed in the near critical region (6.1 MPa to 6.4 MPa at 298.15 K). When the vapor and liquid phase is in equilibrium, the chemical potential and Gibbs free energy of both phases are equal for pure fluids, and they are thermally and physically in equilibrium. The calculated molar volumes of liquid (n L ) and vapor (n v ) phases by PR-EoS at a given temperature and pressure were used to calculate the volume fraction (v F ) of vapor phase CO 2 following: 22,52 v n n n where n L and n v are the molar volumes of liquid and vapor phases, respectively, and they are calculated using PR-EoS for a given pressure and temperature. The volume fraction ratio of vapor (v F ) and liquid CO 2 was used to calculate the total number of moles injected at near critical phase region (6.1 MPa to 6.4 MPa at 298.15 K).

Evaluation of CO 2 Adsorption by Langmuir and BET Isotherm
where P eq is equilibrium pressure (Pa), m eq is the mass of CO 2 adsorbed at given equilibrium pressure (g/kg), m ∞ is limiting value of mass adsorbed (maximum adsorption capacity), also mass of a maximum monolayer adsorbate covering the surface of the sorbent (g/kg), and b is the Langmuir parameter, which is also reciprocal of half-loading pressure, (Pa −1 ). In this study, m ∞ and b values were obtained from nonlinear regression analysis. The thermodynamic parameters, e.g., energy of adsorption and Gibbs free energy were calculated from the Langmuir parameters (m ∞ and b) as 56 where b 0 is the exponential factor (Pa −1 ), ΔH ad is energy of adsorption (J/mol), τ 0 is vibration period related to the residence time of the adsorbed CO 2 molecule (typically on the order of 10 −13 s), N m is the number of molecules adsorbed (related to m ∞ and Avogadro's number), σ A is cross sectional area covered by one CO 2 molecule (m 2 ), M is molecular mass of CO 2 (0.04401 kg/mol). The Gibbs free energy (ΔG ad 0 , kJ/mol) can be calculated as 56 The nonlinear form of the BET model is expressed as 59 where n is the amount of gas adsorbed (mol), n mon is number of moles to cover monolayer adsorption (mol), P eq is the equilibrium pressure (Pa), P 0 is the saturation pressure (7.39 × 10 6 Pa), c is dimensionless parameter related to energy of adsorption ΔH ad . The c and n mon values were obtained from nonlinear regression analysis. The dimensionless parameter c is related to the adsorption energy and is defined as 59 The tick mark represents the experiments conducted.

ACS
where Q 1 is the adsorption energy on a bare surface (monolayer adsorption) (J/mol), and Q 2 is the energy of second and subsequent layers (J/mol). The surface area of 1 mol of CO 2 in the liquid state is calculated as 60,61 where a s is effective surface area covered by 1 mol of CO 2 (m 2 / mol), and V m L is liquid molar volume of CO 2 (m 3 /mol). The number 1.091 is the packing factor of 12 neighboring molecules in a bulk liquid and six on a plane. 60 A s is the specific surface area (m 2 /kg), and n mon is number of moles required to complete the monolayer coverage per kg of coal sample, mol/kg.

Adsorption−Desorption Kinetics.
The data obtained from the experimental program (Table 2) were fitted into pseudo-first-order (PSO) and pseudo-second-order rate equations. 62,63 q q e PFO: (1 ) where q t represents the mass of CO 2 adsorbed per unit mass of adsorbent at time t (g of CO 2 /kg of coal), q e represents the mass CO 2 adsorbed per unit mass of adsorbent at equilibrium (g of CO 2 /kg of coal), k is the first-order rate constant (h −1 ), and k 2 is the second-order rate constants (kg g −1 h −1 ). Desorption kinetics data were fitted into modified PFO and PSO equations. The equations are modified on the basis that the amount of CO 2 adsorbed on coal is the rate determining factor. 36 where k d1 is the first-order rate constant for desorption, (h −1 ) and k d2 is the second-order rate constants for desorption (kg g −1 h −1 ).
To predict the influence of pore diffusion mechanism of coal-CO 2 interaction, experimental data were also fitted into the Bangham model. 64 where k b (h −1 ) and n are constants of the model.

Adsorption Capacity of Intact and Powdered Coals at Subcritical and near Critical Conditions.
Adsorption behavior of powder and intact samples of two different ranks are compared here. The adsorption isotherms of 9 ft AB, 18 ft AB, and BP coal samples are presented in Figure  3(a), (b), and (c), respectively for the maximum CO 2 injection pressure up to 6.4 MPa, which is below the critical pressure of CO 2 at 298.15 K. The powder samples of 9 and 18 ft AB anthracite coal exhibited greater CO 2 adsorption than the intact samples (Figure 3a,b). In contrast, the intact bituminous sample of Big Pit coal exhibited similar adsorption behavior to that of the powder sample ( Figure 3c). All the three intact coal samples showed similar adsorption isotherm pattern with 9 ft AB showing slightly higher adsorption capacity (Figure 3d).
The adsorption capacities of powder samples of the 9 and 18 ft AB coal were about 21% and 36% higher than that of intact samples, respectively. The results show that more adsorption sites are available in the powdered samples compared with the intact samples. The case is different when comparing powder and intact for bituminous BP samples. The CO 2 adsorption isotherm pattern of the intact sample was similar to that of powdered samples for experiments conducted up to equilibrium pressures of 3.6 MPa (Figure 3c). Similar behavior for bituminous coal has been reported by , 67 where the adsorption capacity of powdered sample was 14% lower than the intact sample at applied pressure of 3.1 MPa. Zhao et al. (2014) 68 reported that bituminous coal has channellike and interconnected pores. Such pore structures are observed for both high-and low-volatile bituminous coals. Xu et al. (2015) 26 and Tan et al. (2018) 27 suggested that during the sample grinding process, powdered samples lost most of the channel-like fracture network and pore entrance. The porous matrix difference between the intact and powdered samples resulted in comparable adsorption capacities for the bituminous coal.
This analysis indicated that the sample physical nature has an impact on the CO 2 adsorption on coal samples. To visualize the changes in sample structure, the SEM images of the powdered coal samples and intact samples were taken to identify the nano-/micropores. Figure 4 presents the SEM images for BP and 18 ft AB intact and powdered samples. The nanosized channel like pore entrance/fractures are clearly visible in the intact specimens of the bituminous sample ( Figure 4a). However, the channel like pore openings have not been identified in the powdered bituminous BP sample indicating the pulverization of the sample destroys them (Figure 4b,c). The features of intact bituminous sample have not been identified in anthracite intact samples (Figure 4d). The anthracite 18 ft AB powdered samples showed the exposed nanosized pore entrances (Figure 4e,f) which were observed in intact samples as well. Similarly, no discernible differences were found between anthracite 9 ft AB intact and powdered samples (Figure 4g−i). These results are consistent with the adsorption isotherm pattern observed for the intact and powdered samples of the bituminous and anthracite coal samples. As discussed elsewhere, the high-density CO 2 adsorption in channel-like pores of the intact bituminous coal reflected the adsorption capacity ( Figure 3).
The results from the adsorption tests and SEM images clearly showed that the powdered and intact samples of coals considered in this investigation exhibited different adsorption capacities. Therefore, testing intact samples is more appropriate for determining the adsorption capacity since it reflects the fabric and structure of in situ coal seam.
The injection pressure is considered as one of the key parameters that affects the adsorption capacity of coals. For pressures lower than 6.1 MPa, only the gas phase would exist in the system. At higher pressures, that is, near the critical region (6.1 to 6.4 MPa), the coexistence of liquid and vapor phases of CO 2 is evident. The fraction of liquid and gas CO 2 coexisted during the injection were calculated as described in section 2.3.
The adsorption isotherms of 18 ft AB powder and intact coal for an injection pressure range of 0.5 to 6.4 MPa are presented in Figure 3b. It can be seen from Figure 3b that the 18 ft AB intact specimen showed maximum capacity of 3.328 mol of CO 2 /kg of coal (146 g/kg), and the powdered specimen exhibited 1.843 mol of CO 2 /kg of coal (52.12 g/kg). It is noted that, at lower pressures (<6.1 MPa), the powdered sample showed a higher adsorption capacity than the intact sample. However, at a near critical injection pressure range (6.1 to 6.4 MPa), the intact sample showed a higher adsorption capacity than the powder. This is because the condensation and high-density CO 2 adsorption occur in the nanopores and microfractures of intact samples due to the gas cavitation or condensation.  Table 3. Figure 3a−c shows the plots comparing the experimental data of intact and powdered samples of 9 ft AB, 18 ft AB, and BP against results obtained from the Langmuir model. Table 3 summarizes the Langmuir parameters.
At lower and intermediate pressures (<6.1 MPa), there was good agreement between experimental and model results (Figure 3a,c). The experimental results deviated from the model to show the multilayer build-up at high pressures (from 6.1 to 6.4 MPa). This was evident in the intact and powdered samples of 18 ft AB (Figure 3b). These findings support the expected theory of high-density CO 2 adsorption in microporous structure of the intact samples at elevated pressures.
It was explained in the previous section why the bituminous intact coal sample had a similar adsorption capacity as the powdered sample of the same coal, which was reflected in the calculated maximum capacity. The predicted Langmuir maximum adsorption capacity for the BP intact (bituminous) was 53.66 g of CO 2 /kg of coal, while the powdered BP sample was 45.57 g of CO 2 /kg of coal. The inverse of half-loading pressure of all the samples (Langmuir parameter b, Pa −1 ), the predicted pressure at which half of the maximum adsorption capacity can be achieved, ranged from 10 −6 to 10 −7 Pa −1 ( Table  5).
Half-loading pressure is an important economic parameter in coal seam CO 2 storage. 69 Conducting an isobaric adsorption experiment at the half-loading pressure value predicted by the Langmuir model can yield half of the maximum adsorption capacity of the specific coal sample. Experiments at 1.59 MPa (half-loading pressure; reciprocal of the b-value for 18 ft AB intact) can, for example, achieve a loading of half the 86.97 g CO 2 /kg of coal (Figure 3b; Table 3). Similarly, at 0.40 MPa (inverse of the b value for 9 ft AB intact; Figure 3a; Table 3), half of 80.54 g of CO 2 /kg of coal can be loaded.
The observations discussed above imply that the monolayer was covered at pressures less than 1 MPa, and the isotherm pattern observed at intermediate pressures showed the type II isotherm slope 70 rather than the plateau typically observed in Langmuir type adsorption, representing the multilayer build-up that occurs at coal surfaces. 60 The pattern was visible in the intact coal samples because capillary condensation occurs in the pores of the intact samples, and the plots in Figure 3a−c showed a deviating uptrend from the Langmuir model.
The adsorption energy (ΔH ad ) was calculated using the Langmuir parameters obtained from the isotherm model fittings (maximum Langmuir adsorption capacity (m ∞ ) and the constant b). The energy of adsorption values was between −15 kJ/mol and −22 kJ/mol (Table 4), which are attributed to the physical adsorption (enthalpy change is in the range of −20−40 kJ/mol 71 ).
The Gibbs free energy of CO 2 adsorption on coal was calculated and is shown in Table 4. The adsorption energy/ Gibbs free energy of adsorption are molar quantities that increase with the number of moles adsorbed. The findings were directly compared with previously reported findings on an 86% carbon content coal, where the enthalpy of adsorption ranged from 25.3 to 27.3 kJ/mol, 72 which is comparable with the current study's estimated values. The adsorption energy calculated in this work is similar to the numerical values of the heat of condensation of CO 2 (15.8 kJ/mol 73 ), indicating that liquid-like adsorption theories such as BET should be used to explain CO 2 adsorption on coal.  Table 5). This could be the reasons that the intermediate pressure experiments     Table 5 summarizes the calculated available specific surface area on coal for the adsorption of gas molecules. The intact sample of bituminous BP coal (86263 m 2 /kg) showed a higher surface area than the intact samples of anthracite 18 ft AB (78408 m 2 /kg) and lower than the 9 ft AB (121397 m 2 /kg) samples. The powdered samples of 9 ft AB had a higher specific surface area than the powdered samples of 18 ft AB and BP samples. The intact sample of BP (86263 m 2 /kg) exhibited a similar specific microporous surface as the powdered samples of BP (81407 m 2 /kg). This is effect of the bituminous coal structure (microporous porous network volume) on the adsorption of CO 2 in intact bituminous sample which resulted in a higher adsorption capacity. The obtained specific surface areas in the current work (78408 m 2 /kg to 153067 m 2 /kg) are comparable with the specific surface area available for CO 2 obtained by Zhao et al. (2016) 75 (77400 m 2 /kg to 198400 m 2 / kg).

Comparison of Langmuir and Brunauer− Emmet− Teller (BET) Models.
To evaluate the adsorption of CO 2 by the coal samples, the Langmuir and BET models were compared based on the experimental data fitting effect. Nonlinear regression analysis has been used to fit the theoretical models and experimental results. The optimal model is shown by the combination of the correlation coefficient (R 2 ) and standard error of estimation (SEOE) ( Tables 4 and 5). The BET model generally demonstrated good agreement with the experimental results for the intact samples. The experimental findings of powdered 18 ft AB and 9 ft AB anthracite samples fit the Langmuir model quite well. Both the BET and Langmuir models fit well with the experimental data of powder and intact samples of BP bituminous coal.

Kinetics of CO 2 Adsorption on Different Condition and Rank of Coal.
Pseudo-first order (PFO) and pseudosecond order (PSO) kinetic models were used to fit the experimental data (that is, the amount adsorbed CO 2 versus time). The adsorbed CO 2 predicted by the PFO and PSO  models at time t (q t , g adsorbed CO 2 /kg coal) are plotted against the experimental values in Figure 5. Figure 5, panels a−e shows the results obtained for samples of 9 ft AB intact, 9 ft AB powder, 18 ft AB intact, 18 ft AB powder, and Big Pit powder, respectively. Tables 6, 7, and 8 show the rate constants (K ad1 , K ad2 for adsorption, and K de1 for desorption), equilibrium  concentration (q e ), standard error of estimate and R 2 values for the model fit for the 9 ft AB intact, 9 ft AB powder, 18 ft AB dry intact, 18 ft AB powder, and Big Pit powder, respectively. Overall, the plots and the combination of standard error of estimate and correlation coefficient (R 2 ) indicate that the adsorption kinetics data agree well with the PSO model than the PFO model. The PSO model implies that surface interaction and bulk pore diffusion dominate CO 2 adsorption on coal. 76,77 The pressure dependence of K ad2 demonstrated that the pore diffusion being the rate-determining step in the beginning and surface interaction being the slowest rate-determining step at higher pressures (K ad1 , K ad2 values in Tables 6−8). There are only a few other studies to compare the kinetic parameters with. Gabruśet al. (2021) 78 published an experimental study on CO 2 adsorption on bituminous coal in which the results have been fitted into PFO and PSO models. The K ad1 and K ad2 values obtained at 298.15 K and 2 MPa equilibrium pressure were much higher than the values obtained in the current study. K ad1 was in the range of 1613 × 10 3 to 1011 × 10 3 h −1 , and K ad2 was in the range of 5752 × 10 3 h −1 to 11851 × 10 3 h −1 . However, these experiments were conducted for less than 24 h equilibrium time to reach the maximum pressure range of 2 MPa whereas the current study allowed the equilibrium to occur for each pressure steps (0.5 to 6.4 MPa).
Pore diffusion was more pronounced during the desorption kinetics, which fits both the PFO and PSO models well. The rate-limiting step in the desorption process was the slow release of CO 2 molecules trapped in the pores (K de1 values; Table 6). It can be seen from the results presented in Figure 5a that the adsorption−desorption kinetics plots of 9 ft AB intact, the model plot fitted very well with PFO model implying that the rate of desorption depends on the CO 2 trapped in the pores.
In order to explore whether the CO 2 adsorption is influenced by the mass transport phenomena of pore diffusion, the adsorption experimental data of 9 ft AB the Bangham model were used (eq 19). 37,65 The Bangham model assumes that pore diffusion influences the kinetics of the adsorption process. Equation 19 presents the nonlinear form of the model. The correlation coefficient (R 2 ) from the best-fit indicates the pore diffusion and pressure dependency of the constants k b (h −1 ), and n indicates the rate-determining step at the corresponding pressure range. The kinetic data acquired for the intact and powdered samples of 9 ft AB 18 ft AB, and powdered samples of BP were fitted with the model. Figure 6, panels a−e presents results for 9 ft AB intact, 9 ft AB powder, 18 ft AB intact, 18 ft AB powder, and Big Pit powder, respectively.
The higher correlation coefficient (R 2 ) in Figure 6a−e show that the pore diffusion is one of the rate determining steps. The correlation coefficient (R 2 ) value obtained for high pressure experiments up to 6.3 MPa for 18 ft AB coal was 0.84 ( Figure  6c), which was less than the values obtained for lower pressure experiments for 18 ft AB powder (R 2 = 0.98; Figure 6d), 9 ft AB intact (R 2 = 0.98; Figure 6a), 9 ft AB powder (R 2 = 0.98; Figure  6b), and Big Pit powder (R 2 = 0.9; Figure 6e). These findings indicate that at lower pressures, bulk pore diffusion is the primary rate-determining step, while at higher pressures, surface interaction takes over, which is the slowest step. 79 Overall, the experimental data obtained from the current study fitted very well with the PSO kinetic model and Bangham pore diffusion model indicating that surface interaction and pore diffusion/ condensation are the rate-determining steps in the CO 2 adsorption process on coal. The PSO model fit the data better than the Bangham model (based on R 2 and SEOE). However, the PSO model required separate segment fitting of each experimental pressure step up stage, whereas the Bangham model can use the entire data set without fitting each pressure step up stage separately.

Adsorption−Desorption Hysteresis.
The adsorption and desorption isotherms of intact 9 ft AB, intact 18 ft AB, and powdered 18 ft AB coal samples are presented in Figure 7a,b,d. The positive deviation in the hysteresis indicates that some amount of CO 2 still adsorbed in the porous structure of the coal. This pattern also depicts the Type II and H3 adsorption− desorption pattern described by IUPAC classification for the pore diffusion/condensation dominated adsorption process. 70,80 Adsorption hysteresis patterns differ between powder and intact samples of 18 ft AB for experiments up to 6.4 MPa, owing to high-density adsorbed phase formation in the intact coal fracture system and micropores. Comparatively the lower adsorption capacity observed with powdered 18 ft AB shows the effect of the physical nature of the intact sample and the effect of near critical pressure range (6.1 to 6.4 MPa; liquid and gas coexistence) CO 2 adsorption at 298.15 K (Figure 7b,c).
The adsorption−desorption hysteresis patterns were found to be consistent with previous work. 69,81−85 The current study experiments and findings reveal that the physical nature of coal and the thermodynamic nature of CO 2 provide a pathway to a deep pore matrix in which CO 2 molecules are trapped. Because CO 2 can enter through supermicropores (<2 nm), the ink bottle effect was observed in the hysteresis pattern of both intact and powdered samples. 29 As a result, the slow release of CO 2 trapped in the pores is observed as a positive deviation in the adsorption−desorption hysteresis pattern.
The amount of CO 2 that remained in the coal after the desorption experiments demonstrated the coal seams' ability to trap CO 2 . The residual values for intact 9 ft AB, intact 18 ft AB, and powder 18 ft AB coal samples were 46.21 g/kg (1.05 mol/ kg), 39.61 g/kg (0.9 mol/kg), and 51.93 g/kg (1.18 mol/kg), respectively. The higher residual amount of CO 2 adsorbed for the powdered sample for the 18 ft AB was attributed to the adsorption of CO 2 in the exposed (when the samples are powdered) super micropores (<2 nm) and evidence of ink bottle effect. 83 Figure 7d shows pressure versus time curves observed for intact 9 ft AB sample after evacuating the whole adsorption system to create null equilibrium pressure (0 MPa) at 298.15 K indicating the CO 2 entrapment in the pores.
The reversibility of CO 2 and the adsorption desorption hysteresis pattern are influenced by the sample type (intact and powdered) and coal rank. The hysteresis index (HI) values were calculated for 9 ft AB and 18 ft AB coal samples to evaluate the adsorption−desorption as described in Wang et al. (2014) 86 and Wang et al. (2016). 87 The adsorption desorption is completely reversible when HI = 0 and irreversible when HI = 1. Comparing the anthracite 18 ft AB intact and powder, the powder sample showed higher HI values (0.92) than that of intact samples (0.16). However, the low carbon content intact anthracitic sample (9 ft AB) had HI = 0.70. The carbon content is related to the coal rank and pore structure reflected on the desorption pattern. The higher HI (0.92) obtained for the higher rank powdered anthracitic 18 ft AB showed that the nanopores are exposed to CO 2 to enter when powdered indicating the sample physical type plays critical role in the desorption patten.

CONCLUSIONS
The adsorption−desorption isotherm patterns and kinetics of powdered and intact specimens of anthracite (9 ft AB and 18 ft AB) and bituminous (BP) coals obtained at the subcritical pressure range (up to 6.4 MPa) of CO 2 at temperature of 298.15 K using the manometric/volumetric adsorption measurement method were presented in this study.
• The CO 2 adsorption capacity of powdered samples of anthracite samples showed a higher adsorption capacity than that of intact samples due to the increased surface area which exposes the polarizing sites of anthracite coal and the nanopores. • The intact bituminous (BP) coal showed a similar adsorption capacity as the powdered samples. Pulverizing the sample destroys the microfracture channel-like network that is specific to bituminous coals, and the results observed in this study demonstrated the effect of different porous networks of anthracite and bituminous coal samples on the CO 2 adsorption capacity. • The experiments conducted at the near critical region (up to 6.4 MPa) showed that the intact samples exhibited a type II adsorption isotherm pattern with an upward trend, and the powdered sample showed a monolayer type plateau indicating the sample's physical nature had an impact on the type of the isotherm that occurs. • Overall, the fitting of the adsorption experimental data and the theoretical model in this paper show that the BET model fits better than the Langmuir model. • Within the coal rank, the reversibility of the CO 2 and hysteresis pattern were affected by the sample type (intact and powder). The powdered samples of anthracitic sample showed a higher degree CO 2 irreversibility than the intact sample indicating the CO 2 entrapment in the exposed nanopores. The analysis indicated that the experiments with large undisturbed samples are needed to test the adsorption capacity of specific coal type. The experimental results were fitted to PFO, PSO, and Bangham pore diffusion kinetic models, which showed that surface interaction and pore diffusion mechanisms are the rate-determining mechanisms of CO 2 -coal adsorption processes. Overall, the paper explored the effect of physical nature and subcritical pressure adsorption of CO 2 at 298.15 K in the context of CO 2 sequestration in shallow level coal seams.